DSM Engineering Plastics
– Technical Guide
Cantilever beam snap-fits
Cantilever beam type snap-fits can be calculated using a simplification of the general beam theory. However the calculations are a simplification. In general, the stiffness of the part to which the snap-fit connects, is important. The formulae mentioned only roughly describe the behavior of both the part geometry and the material. On the other hand, the approach can be used as a first indication if a snap-fit design and material choice are feasible.
Cantilever beam with constant rectangular cross section
A simple type of snap-fit, the cantilever beam, is demonstrated in the figure below, which shows the major geometrical parameters of this type of snap-fit. The cross section is rectangular and is constant over the whole length L of the beam.
The maximum allowable deflection y and deflection force F b
can be calculated with the following formulas if the maximum allowable strain level ε of the material is known.
2 L
2 y = -- . -- . ε
3 t
w . t
2
. E
F b
6 . L s
= ------------ . ε
Date:23 February, 2005
1
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide
E where s
= secant modulus
L = length of the beam t = height of the beam w = width of the beam
ε = maximum allowable strain level of the material
The four dimensions that can be changed by the designer are:
- h
, the height of the snap-fit lip. Changing the height might reduce the ability of the snap-fit to ensure a proper connection.
- t
, the thickness of the beam. A more effective method is to use a tapered beam. The stresses are more evenly spread over the length of the beam.
- increasing the beam length,
L
, is the best way to reduce strain as it is represented squared in the equation for the allowable deflection.
- the deflection force is proportional to the width, w , of the snap-fit lip.
Beams with other cross sections
The following general formulae for the maximum allowable deflection y and deflection force F cantilever beams with a constant asymmetric cross section. b
can be used for
L
2 y = ------- . ε
3 . e
E
F b s
e . L where
. I
= ------- . ε
E s
= secant modulus
I = moment of inertia of the cross section
L = length of the beam e = distance from the centroid to the extremities
ε = maximum allowable strain level of the material
Normally tensile stresses are more critical than compressive stresses. Therefore the distance from the centroid to the extremities, e, that belongs to the side under tension is used in the above-mentioned formulae.
The moment of inertia and the distance from the centroid to the extremities is given in table 1 for some cross sections.
Date:23 February, 2005
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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide
Table 1. Moment of inertia and distances from centroid to extremities
Date:23 February, 2005
3
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide
Tapered beams with a variable height
The following formulae can be used to calculate the maximum allowable deflection y and the deflection force
F b
for a tapered cantilever beam with a rectangular cross section. The height of the cross section decreases linearly from t
1
2 . L 2
to t
2
, see figure above. y = c .-------- . ε
3 . t
1
w . t
1
2
F b
= -------------- . ε
6 . L where
. E s
E s
= secant modulus
L = length of the beam c = multiplier w = width of the beam t
1
= height of the cross section at the fixed end of the beam
ε = maximum allowable strain level of the material
The formula for the deflection y
contains a multiplier c
that depends on the ratio t the height of the beam at the fixed end and t
2
2
/ t
1
, see table 2, where t
is the height of the beam at the free end.
1
is
Date:23 February, 2005
4
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide t
Table 2. Multiplier c as a function of the height
2
/ t
1
0.40 0.50 0.60 0.70 0.80 0.90 1.00
Tapered beams with a variable width
The following formulae can be used to calculate the maximum allowable deflection y
and deflection force
F b for a tapered cantilever beam with a rectangular cross section. The width of the cross section decreases linearly from w
1
to w
2
, see figure above.
2 . L 2 y = c .-------- . ε
3 . t
w
1
. t
2
. E
F b
6 . L s
= -------------- . ε
E where s
= secant modulus
L = length of the beam c = multiplier w
1
= width of the beam at the fixed end of the beam t = height of the cross section
ε = maximum allowable strain level of the material
Date:23 February, 2005
5
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide
The multiplier c depends on the ratio w
2 and w
2
/ w
1
, see table 3, where w
1
is the width of the beam at the fixed end
is the width of the beam at the free end.
Table 3. Multiplier c as a function of the width w
2
/ w
1 c 1.368 1.284 1.158 1.000
Cylindrical snap-fits
One must distinguish between a cylindrical snap-fit close to the end of the pipe or remote from the end
Date:23 February, 2005
6
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide
More material must be deformed if the snap fit is remote from the end, and the deflection force F b
and mating force F a
will be a factor 3.4 higher. The snap-fit is regarded as being remote if l > 1.8 . √ ( D . t ) where l = distance to the end of the pipe.
The following symbols are further used:
D = average diameter of the pipe = (D o
+ d o
) / 2
D d d i o o
= outside diameter of the pipe
= outside diameter of the shaft
= inside diameter of the shaft
Δ d / 2 = height of the bulge on the shaft = depth of the groove in the pipe
E s
= shear modulus of the plastic t = wall thickness of the pipe = (D
μ = coefficient of friction
ν = Poisson’s ratio of the plastic o
– d o
) / 2
The formula for the deflection force F b
is given in table 4 for both a rigid (metal) shaft with a flexible pipe, and a flexible shaft with a rigid (metal) pipe. Four cases can be distinguished.
Date:23 February, 2005
7
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide
Table 4. Deflection force F
Rigid shaft, flexible pipe b
Snap-fit close to the end Flexible shaft, rigid pipe
Snap-fit r emote from the end
Rigid shaft, flexible pipe
Flexible shaft, rigid pipe
0.62 . Δ d . d
√
[(D o
[(D
/ d o
/ d o
- 1) / (D o
/ d o
+ 1)] o
. --------------------------------------------- . E o
) 2 + 1] / [(D o
/ d o
) 2 – 1] + ν s
0.62 . Δ d . d o
√
. --------------------------------------------- . E
[(d
[(d o
/ d o
/ d i
) i
- 1) / (d
2 + 1] / [(d o o
/ d
/ d i
) i
+ 1)]
2 – 1] – ν s
2.1 . Δ d . d o
. --------------------------------------------- . E
[(D o
√ [(D
/ d o
) o
2
/ d o
- 1) / (D
+ 1] / [(D o o
/ d
/ d o
)
2 o
+ 1)]
– 1] + ν s
2.1 . Δ d . d o
√
[(d o
[(d
/ d o i
)
/ d
2 i
- 1) / (d
+ 1] / [(d o o
/ d
/ d i i
+ 1)]
. -------------------------------------------- . E
)
2
– 1] – ν s
If the deflection force F b expression
according table 4 has been calculated, the mating force F a
is found using the
μ + tan α
F a
= F b
1
. -----------------
1 – μ . tan α
1
The highest tangential strain ε
- Rigid shaft, flexible pipe: ε
φ
in the plastic is approximately:
- Flexible shaft, rigid pipe: ε
φ
= Δ d / d
φ o
(tension in the pipe)
= - Δ d / d
The highest axial bending strain ε a o
(compression in the shaft)
in the plastic is about a factor 1.59 higher :
ε a
= 1.59 . ε
φ
(tension at one side and compression at the other side)
The calculation procedure when both parts are flexible and both are deformed is explained in the theory of snap fits . As a first approach, for flexible materials with a comparable stiffness, one can assume that the total deformation Δ d is equally divided between the two parts.
Spherical snap-fits
The spherical snap-fit can be regarded as a special case of the cylindrical snap-fit. The formulas for a cylindrical snap-fit close to the end of the pipe can be used.
Date:23 February, 2005
8
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.

DSM Engineering Plastics
– Technical Guide
Mold construction
Mold construction costs are highly affected by the design of the snap fit.
For design A, an expensive slide in the mold is required and the flat surfaces require expensive milling. No slide is required for alternative B and the cylindrical outside surface can simply be drilled.
Date:23 February, 2005
9
All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and shall verify quality and other properties or any consequence from the use of all such information.